Microlocal Analysis and Precise Spectral Asymptotics

Häftad, Engelska, 2010

Av Victor Ivrii

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This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished

Produktinformation

Utgivningsdatum2010-12-04
Mått155 x 235 x 41 mm
Vikt1 118 g
FormatHäftad
SpråkEngelska
SerieSpringer Monographs in Mathematics
Antal sidor733
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783642083075

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Beräkning och matematisk analys inom Naturvetenskap och teknik

0. Introduction.- I. Semiclassical Microlocal Analysis.- 1. Introduction to Semiclassical Microlocal Analysis.- 2. Propagation of Singularities in the Interior of a Domain.- 3. Propagation of Singularities near the Boundary.- II. Local and Microlocal Semiclassical Asymptotics.- 4. LSSA in the Interior of a Domain.- 5. Standard LSSA near the Boundary.- 6. Schrödinger Operators with Strong Magnetic Field.- 7. Dirac Operators with Strong Magnetic Field.- III. Estimates of the Spectrum.- 8. Estimates of the Negative Spectrum.- 9. Estimates of the Spectrum in an Interval.- IV. Asymptotics of Spectra.- 10. Weylian Asymptotics of Spectra.- 11. Schrödinger, Dirac Operators with Strong Magnetic Field.- 12. Miscellaneous Asymptotics.- References.

From the reviews: "The monograph, under review, deals with one of the central problems in the spectral theory of partial differential operators, namely with the problem of spectral asymptotics, in particular with the problem of the asymptotic distribution of eigenvalues. ... Summarizing, this is an excellent monograph on microlocal analysis, propagation of singularities and spectral asymptotics, based mainly on the author's own results. It is warmly recommended to specialists in PDE's, theoretical physics. The monograph will be useful also for advanced students." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 74, 2008)